Algebra with Exponents - Binomial over Binomial and Constant

Level 1

This math topic focuses on practicing algebra with exponents, specifically solving expressions where a binomial raised to an exponent is equated to a constant. The problems include simplifying and solving for variables such as z, w, y, p, and x, where the exponent involves a quotient of binomials. Each problem is set in the context of negative, fractional, and power laws of exponents, encouraging the development of skills in manipulating complex algebraic expressions involving powers.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Algebra with Exponents - Binomial over Binomial and Constant Worksheet

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Algebra with Exponents - Binomial over Binomial and Constant
1
A LaTex expression showing {{3}} to the power of {(\frac{{z + 7 }{{z - 6}})}} = 9
Simplify and solve for z
a A LaTex expression showing z = 19
b A LaTex expression showing z = 20
2
A LaTex expression showing {{5}} to the power of {(\frac{{w - 9 }{{w - 3}})}} = 25
Simplify and solve for w
a A LaTex expression showing w = -2
b A LaTex expression showing w = -3
3
A LaTex expression showing {{2}} to the power of {(\frac{{y + 8 }{{y - 7}})}} = 16
Simplify and solve for y
a A LaTex expression showing y = 11
b A LaTex expression showing y = 12
4
A LaTex expression showing {{5}} to the power of {(\frac{{w - 3 }{{w - 7}})}} = 25
Simplify and solve for w
a A LaTex expression showing w = 11
b A LaTex expression showing w = 12
5
A LaTex expression showing {{3}} to the power of {(\frac{{p - 4 }{{p - 5}})}} = 9
Simplify and solve for p
a A LaTex expression showing p = 7
b A LaTex expression showing p = 6
6
A LaTex expression showing {{2}} to the power of {(\frac{{x + 6 }{{x - 8}})}} = 8
Simplify and solve for x
a A LaTex expression showing x = 14
b A LaTex expression showing x = 15
7
A LaTex expression showing {{3}} to the power of {(\frac{{w + 5 }{{w - 8}})}} = 9
Simplify and solve for w
a A LaTex expression showing w = 21
b A LaTex expression showing w = 22
8
A LaTex expression showing {{3}} to the power of {(\frac{{t + 8 }{{t - 5}})}} = 9
Simplify and solve for t
a A LaTex expression showing t = 18
b A LaTex expression showing t = 20